As the penetration of distributed photovoltaic (PV) generation continues to increase in modern power systems, low-voltage distribution station areas face significant challenges related to voltage regulation. The stochastic and intermittent nature of solar irradiance leads to mismatches between peak generation and peak load periods, often resulting in overvoltage conditions that exceed safe operating limits. This paper presents a comprehensive automatic overvoltage control method specifically designed for low-voltage distribution station areas, leveraging the reactive power capability of solar inverters. By coordinating solar inverters with on-load tap changers (OLTC), the proposed method effectively mitigates overvoltage while minimizing network losses and reducing photovoltaic curtailment. Extensive simulations demonstrate that the voltage control deviation remains below 1.45%, network losses are kept within 15 kW/h, and the power factor consistently exceeds 60%. The approach ensures reliable and efficient operation of distribution systems under various load and generation scenarios.
Introduction
The integration of distributed solar inverters into low-voltage distribution networks has transformed the operational landscape of power systems. However, the inherent variability of solar power generation introduces voltage fluctuations that can exceed permissible limits, leading to overvoltage risks. Traditional voltage regulation methods, such as capacitor banks and tap changers, often lack the response speed and granularity required for modern high-PV penetration scenarios. Solar inverters, which are essential for connecting PV arrays to the grid, possess the capability to absorb or inject reactive power, making them ideal candidates for voltage support. This paper focuses on developing an automatic control strategy that fully exploits the reactive power capacity of solar inverters to address overvoltage events in low-voltage distribution station areas.
The proposed method first evaluates the reactive power adequacy of the distribution network using a newly defined index called reactive power sufficiency δOV. Based on this evaluation, the control system decides whether to operate solar inverters independently or in coordination with OLTC. When the reactive power capacity is sufficient, solar inverters perform local voltage regulation using a piecewise control law. When capacity is insufficient, OLTC adjusts the voltage to bring it within the controllable range of the inverters. Additionally, an optimization framework minimizes the total reactive power output of solar inverters while ensuring that node voltages remain close to the rated value. The entire control scheme is automated and operates in real time, ensuring rapid response to changing network conditions.
Reactive and Active Power Regulation Characteristics of Solar Inverters
A typical grid-connected PV system consists of PV arrays, a DC/DC converter, and a DC/AC solar inverter. The solar inverter is the key component that enables bidirectional power flow and voltage control. In normal operation, the active power output of the solar inverter is always less than its rated capacity, leaving a reserve for reactive power generation. The relationship between the active and reactive power outputs is constrained by the inverter’s apparent power rating:
$$
S_i^2 = P_i^2 + Q_i^2
$$
where \(S_i\) is the rated apparent power, \(P_i\) is the active power, and \(Q_i\) is the reactive power of the solar inverter at node \(i\). The reactive power capability is therefore bounded by:
$$
-\sqrt{S_i^2 – P_i^2} \leq Q_{i,t}’ \leq \sqrt{S_i^2 – P_i^2}
$$
The solar inverter can absorb reactive power (inductive mode) when the voltage is high, and inject reactive power (capacitive mode) when the voltage is low. This capability forms the foundation for voltage regulation in distribution networks. The following table summarizes the typical parameters of a low-voltage distribution station area used in this study:
| Parameter | Value |
|---|---|
| Voltage level (V) | 220 |
| Line resistance (Ω/km) | 0.50 |
| Line inductance (H) | 0.315 |
| Voltage upper limit (V) | 230 |
| Voltage lower limit (V) | 210 |
| Solar inverter rated capacity (MW) | 3 |
Coordinated Control Strategy for Solar Inverters and OLTC
Before deploying the solar inverter for overvoltage control, the system must assess the reactive power adequacy of the low-voltage distribution station area. The reactive power sufficiency index is defined as:
$$
\delta_{OV} = \frac{1}{\sum_{j \in \{PV\}} R_{i,j,U-Q} Q_i^{\max}} (U_{PV,\max} – U_{PV,th})
$$
where \(U_{PV,\max}\) and \(U_{PV,th}\) are the maximum photovoltaic node voltage and the upper threshold for voltage violation, respectively; \(\sum_{j \in \{PV\}} R_{i,j,U-Q}\) is the sum of voltage-to-reactive power sensitivities; and \(Q_i^{\max}\) is the maximum reactive power output of the solar inverter. If \(\delta_{OV} < 1\), the reactive power capacity is sufficient; otherwise, coordination with OLTC is required.
Local Control by Solar Inverters Alone
When the reactive power capacity is adequate, the solar inverter performs local voltage control according to the following piecewise function:
$$
Q_{i,t}’ =
\begin{cases}
-Q_i^{\max}, & U_{i,t} \geq U_{cr,2+} \\
-Q_i^{\max} \frac{U_{i,t} – U_{cr,1+}}{U_{cr,2+} – U_{cr,1+}}, & U_{cr,1+} \leq U_{i,t} \leq U_{cr,2+} \\
0, & U_{cr,1-} \leq U_{i,t} \leq U_{cr,1+} \\
Q_i^{\min} \frac{U_{i,t} – U_{cr,1-}}{U_{cr,2-} – U_{cr,1-}}, & U_{cr,2-} \leq U_{i,t} \leq U_{cr,1-} \\
Q_i^{\min}, & U_{i,t} \leq U_{cr,2-}
\end{cases}
$$
Here, \(U_{cr,1+}\) and \(U_{cr,1-}\) are the control thresholds for starting reactive power regulation, while \(U_{cr,2+}\) and \(U_{cr,2-}\) define the voltage boundaries for full reactive power output. When the node voltage exceeds \(U_{cr,1+}\), the solar inverter absorbs reactive power to prevent further voltage rise. When the voltage falls below \(U_{cr,1-}\), the inverter injects reactive power to support the voltage.
OLTC-Solar Inverter Coordination
If the reactive power capacity of solar inverters is insufficient, coordination with OLTC becomes necessary. Two scenarios are considered:
- Uniform voltage violation across lines: The OLTC first adjusts the tap position to bring the voltage within the controllable range of the solar inverter. The control function is:
$$
F_t = T_t \quad \text{if } U_{oltc,n+} \leq U_{t,\max} \leq U_{oltc,m+} \text{ or } U_{oltc,m-} \leq U_{t,\min} \leq U_{oltc,n-}
$$
After the OLTC adjustment, the solar inverter performs local control as described above.
- Diverse voltage violations across lines: The solar inverters first perform local control to reduce the voltage deviation disparity. Then, the overall voltage violation statistics determine the OLTC action. The control direction is based on the maximum violation sum, and the tap position is determined by the most severe node voltage:
$$
F_{t+\Delta t} =
\begin{cases}
\phi\left( \sum_{i \in O} \Delta U_i \right) & \text{if } \sum_{i \in O} \Delta U_i \geq \sum_{j \in D} \Delta U_j \text{ and } U_{oltc,n+} \leq U_{t,\max} \leq U_{oltc,m+} \\
\phi\left( \sum_{j \in D} \Delta U_j \right) & \text{if } \sum_{i \in O} \Delta U_i \geq \sum_{j \in D} \Delta U_j \text{ and } U_{oltc,m-} \leq U_{t,\min} \leq U_{oltc,n-}
\end{cases}
$$
where \(O\) and \(D\) are the sets of nodes with voltage exceeding the upper and lower limits, respectively; \(\Delta U_i\) and \(\Delta U_j\) are the voltage violation magnitudes; and \(\phi(\cdot)\) is the OLTC control function.
Optimization of Overvoltage Control
To improve the efficiency of overvoltage control, an optimization framework is introduced. The objectives are to minimize the total reactive power output of the solar inverters while bringing node voltages as close as possible to the rated voltage. The dual-objective functions are:
$$
f_1 = \min \sum_{i=1}^{n} Q_{i,t}’
$$
$$
f_2 = \min \sum_{i=1}^{n} \left( \frac{U_{PV} – U_N}{U_{\max}’ – U_{\min}’} \right)^2
$$
where \(f_1\) minimizes the sum of reactive power from all solar inverters, and \(f_2\) minimizes the normalized voltage deviation of PV nodes from the rated value \(U_N\). The constraints include power flow equations, inverter capacity limits, and reactive power limits:
- Power flow constraints:
$$
P_i = U_i \sum_{j \in H} U_j (G_{ij} \cos \theta_{ij} + B_{ij} \sin \theta_{ij})
$$
$$
Q_i = U_i \sum_{j \in H} U_j (G_{ij} \cos \theta_{ij} – B_{ij} \sin \theta_{ij})
$$
- Solar inverter capacity constraint:
$$
-\sqrt{S_i^2 – P_i^2} \leq Q_{i,t}’ \leq \sqrt{S_i^2 – P_i^2}
$$
- Reactive power capacity constraint:
$$
Q_i^{\min} \leq Q_{i,t}’ \leq Q_i^{\max}
$$
The two objective functions are combined into a single weighted objective using weighting factors \(\omega_1\) and \(\omega_2\) (with \(\omega_1 + \omega_2 = 1\)):
$$
\min F = \omega_1 f_1 + \omega_2 f_2
$$
An improved particle swarm optimization (PSO) algorithm is employed to solve this optimization problem. The optimized control commands are then dispatched to each solar inverter in real time, enabling automatic overvoltage mitigation.
Simulation Results and Analysis
The proposed method is tested on a low-voltage distribution station area with the topology shown previously. The system includes 15 nodes with multiple distributed solar inverters. Three operating scenarios are considered: normal operation, load operation, and heavy-load operation. The voltage instability severity index \(VSI\) is used to evaluate the control performance:
$$
VSI = \frac{1}{N(T – T_c)} \sum_{i=1}^{N} \sum_{t=T_c}^{T} VDI_{i,t}
$$
where \(N\) is the number of lines, \(T_c\) and \(T\) are the fault clearing and end times, and \(VDI_{i,t}\) is the voltage deviation index. Table 2 presents the VSI results for different numbers of overvoltage nodes.
| Operating Time (h) | VSI (%) for 5 nodes | VSI (%) for 10 nodes | VSI (%) for 15 nodes |
|---|---|---|---|
| 2 | 0.44 | 0.64 | 0.80 |
| 4 | 0.58 | 0.70 | 0.82 |
| 6 | 0.30 | 0.42 | 0.58 |
| 8 | 0.68 | 0.70 | 0.84 |
| 10 | 0.38 | 0.40 | 0.59 |
| 12 | 0.64 | 0.76 | 0.84 |
| 14 | 0.30 | 0.58 | 0.78 |
| 16 | 0.64 | 0.76 | 0.82 |
| 18 | 0.40 | 0.60 | 0.96 |
| 20 | 0.42 | 0.68 | 0.90 |
The results demonstrate that the proposed method effectively limits VSI well below the threshold under all node configurations, confirming robust overvoltage control.
Table 3 shows the voltage control results for two cases: uniform voltage control demand and diverse voltage control demand across lines. The voltage violation ratio varies from 2% to 20%.
| Voltage Violation Ratio (%) | Controlled Voltage (V) – Uniform Demand | Controlled Voltage (V) – Diverse Demand |
|---|---|---|
| 2 | 222.20 | 220.00 |
| 4 | 220.00 | 221.00 |
| 6 | 228.10 | 224.60 |
| 8 | 222.00 | 225.50 |
| 10 | 225.00 | 227.00 |
| 12 | 220.00 | 230.00 |
| 14 | 228.60 | 222.00 |
| 16 | 227.40 | 220.00 |
| 18 | 221.00 | 224.20 |
| 20 | 224.10 | 223.00 |
All controlled voltages remain within the allowable range of 210 V to 230 V, proving the effectiveness of the coordinated solar inverter and OLTC control.
Voltage Control Deviation Under Different Operating Conditions
Table 4 describes the three operating scenarios: normal, load, and heavy-load. Table 5 presents the voltage control deviation for 10 sample nodes under each scenario.
| Scenario | Description | Expected Performance |
|---|---|---|
| Normal operation | Stable voltage, small deviations | Accurate control |
| Load operation | Increased load, slight voltage rise | Good adaptability |
| Heavy-load operation | Peak load, significant voltage rise near limits | Requires enhanced control |
| Node Sample | Normal Operation | Load Operation | Heavy-Load Operation |
|---|---|---|---|
| 1 | 1.18 | 1.00 | 0.79 |
| 2 | 0.53 | 0.74 | 1.35 |
| 3 | 0.45 | 1.09 | 0.51 |
| 4 | 1.27 | 0.77 | 0.90 |
| 5 | 0.92 | 1.45 | 0.50 |
| 6 | 0.71 | 0.97 | 1.15 |
| 7 | 0.54 | 1.24 | 0.65 |
| 8 | 1.23 | 0.76 | 0.70 |
| 9 | 1.38 | 1.18 | 0.55 |
| 10 | 0.51 | 1.08 | 0.89 |
The maximum deviation recorded is 1.45% under load operation, which is well within the acceptable tolerance. The coordination between solar inverters and OLTC ensures that even under heavy load, the voltage remains stable.
Network Loss, Curtailment, and Power Factor
Table 6 summarizes the network loss (kW·h), PV curtailment (%), and power factor index (%) for different overvoltage ratios. The power factor index is defined as:
$$
\psi = \frac{\zeta}{M} \times 100\%
$$
where \(\zeta\) is the number of sampling points where the power factor at the transformer exit lies within the range (-0.95, +0.95), and \(M\) is the total number of sampling points. The standard requires network loss below 15 kW·h, curtailment below 15%, and power factor above 60%.
| Voltage Violation Ratio (%) | Network Loss (kW·h) | PV Curtailment (%) | Power Factor Index (%) |
|---|---|---|---|
| 2 | 4.40 | 5.50 | 62.60 |
| 4 | 6.20 | 7.60 | 63.10 |
| 6 | 3.70 | 10.10 | 61.70 |
| 8 | 5.60 | 9.50 | 63.30 |
| 10 | 9.40 | 10.00 | 64.20 |
| 12 | 11.20 | 9.00 | 61.90 |
| 14 | 9.50 | 8.50 | 62.90 |
| 16 | 10.70 | 7.60 | 61.80 |
| 18 | 12.60 | 10.50 | 60.90 |
| 20 | 13.70 | 8.00 | 63.00 |
All metrics satisfy the operational standards. The network loss remains below 15 kW·h, the curtailment is at most 10.6%, and the power factor always exceeds 60%. This indicates that the proposed automatic overvoltage control method utilizing solar inverters is both efficient and practical for real-world distribution networks.
Conclusion
This paper has presented an automatic overvoltage control method for low-voltage distribution station areas that leverages the reactive power capability of solar inverters. By coordinating solar inverters with OLTC, the method adapts to both uniform and diverse voltage violation conditions across different feeders. An optimization framework minimizes reactive power usage while maintaining voltages close to the rated value. Comprehensive simulations under various operating scenarios demonstrate that the voltage control deviation stays below 1.45%, network losses are limited to 15 kW·h, and PV curtailment is significantly reduced. The power factor index consistently exceeds 60%, confirming that unnecessary reactive power waste is avoided. The proposed approach is highly effective for automatic overvoltage mitigation in distribution systems with high penetration of distributed solar inverters, ensuring stable and efficient operation.